Previous studies of BEC in these systems largely rely on the semiclassical Maxwell–Boltzmann equations describing the average population of exciton-polariton states [1]}, [2]}, [3]}, [4]}, [5]}, other mean-field theories [6]}, [7]}, [8]}, and an approach beyond mean-field theory [9]} that takes into account the higher-order correlations.
However, in such treatments, information about the correlations between different polariton states is lost.
In many cases, the driven dissipative Gross–Pitaevskii equation with noise successfully describes the dynamics of BEC [10]}.
However, the Gross–Pitaevskii equation works well only when temperature is well below the condensation temperature [10]}.
This means that it cannot accurately describe the crossover and buildup of coherence.
